Electro-Optic (EO) modulators are useful for applications such as fiber-optic communications (i.e., the telecom industry) particularly if they are power-wise efficient. A reduction in modulator drive power can mean lower cost since lower power (and hence less expensive) electronics can be used to drive and control such modulators, thereby reducing the overall cost of the transmitters in fiber-optic networks. For modulators having sufficiently low full-scale drive voltage (approximately 1-2 volts), those modulators can be driven directly by low-power, low-noise electronic circuits implemented in, for example, InP, CMOS and bi-CMOS technologies. Voltage-efficient EO modulators also will improve the RF-to-RF gain and reduce the noise figure of analog RF-photonic links. Such analog links are useful for many analog cable TV systems as well as for the RF-over-fiber distribution systems being implemented for wireless (e.g., wideband cellular telephone) communications networks. Analog RF-photonic links also are useful for defense-related antenna remoting applications, for photonic control of antenna beams, and in photonic methods for RF signal processing (such as analog-to-digital conversion). Also, digital photonic links, especially ones that can interface directly to low-power electronic circuits, are useful for sensor remoting applications.
A typical Mach-Zehnder interferometric modulator has input light that is split between two EO waveguides. The refractive index of the electro-optically active material in one or both of these two EO waveguides is modulated by a voltage waveform applied to electrodes that are electro-optically coupled to the EO waveguides. The applied voltage produces a change in the electric field (or E-field) across the modulated EO waveguide. The refractive index of the EO material can be varied by varying the E-field at the EO material. The refractive-index modulation is proportional to 0.5n3rΔE, where n is the optical refractive index of the EO material, r is the EO modulation coefficient of the EO material and ΔE is the change in the E-field at the EO material. The phase of the light at the output end of each phase-modulation arm is modulated by modulating the refractive-index of the material in that arm. The Mach-Zehnder interferometer combines the light output from the ends of its two phase-modulation arms in such a way that the intensity of the combined output light depends on the relative phases of the light in the two arms. When a Mach-Zehnder modulator is modulated in push-pull manner, a given applied voltage produces a positive change in the refractive index of one of the phase-modulation arms and produces a negative change in the refractive index of the other phase-modulation arm. With push-pull modulation, the relative EO phase change Δϕp-p produced at the output ends of the two phase-modulation arms is given by:
            Δ      ⁢                          ⁢              φ                  p          -          p                      =                  (                  2          ⁢                      π            /                                                  ⁢            λ                          )            ⁢              n        3            ⁢      r      ⁢                          ⁢      2      ⁢                          ⁢      ΓΔ      ⁢                          ⁢      EL        ,
where L is the length of the actively modulated portion of the phase-modulation arms and λ is the wavelength of the light whose phase is being modulated. Γ describes the percentage overlap between the optical field of the light being modulated and the active EO material whose refractive index is being changed according to the E-field, ΔE, resulting from the applied modulation-control voltage.
One way to achieve this push-pull modulation is by having opposite poling of the EO materials in the two phase-modulation arms. Essentially, the EO modulation coefficient is positive for one arm but is negative for the other arm. Another way to achieve push-pull modulation is to have an electrode structure that produces an E-field that is oriented in one direction in one phase-modulation arm and is oriented in the opposite direction in the other phase-modulation arm, with the EO materials in both arms poled in the same direction. When the two phase-modulation arms have the same poling, the electro-optic dipoles of the EO materials in both arms are oriented in approximately the same direction. However, then the two phase-modulation arms have opposite poling, the electro-optic dipoles of the EO material in one phase-modulation arm are oriented in the opposite direction from the orientation of the electro-optic dipoles of the EO material in the other phase-modulation arm.
A prior art EO modulator with two oppositely poled EO waveguides is described in articles by W. Wang, et al. (“Push-pull poled polymer Mach-Zehnder modulators with a single microstrip line electrode,” IEEE Photonics Technology Letters, vol. 11, no. 1, January 1999, pp. 51-53) and by Y. Shi, J. H. Bechtel and W. Wang (“Low halfwave voltage electrooptic polymer modulators: design and fabrication,” Proceedings of SPIE, Volume 3796 (1999), pp. 336-344). This Mach-Zehnder interferometric modulator has polymer EO material in its two phase-modulation arms poled in opposite directions, as illustrated in FIG. 1a (the poling directions are indicated by the arrows in the solid boxes which solid boxes represent the polymer EO material). The modulator has a microstrip line electrode with a narrower strip conductor located on the top surface and a wider ground conductor located between the optical waveguiding structure and the substrate. The optical waveguide of each phase-modulation arm contains a shallow-rib waveguide embedded in cladding layers, as shown in FIG. 1b. The thickness of the guiding layer is approximately 1.5 μm to 2.5 μm and the overall distance between the two electrodes of the microstrip line is approximately 10 μm. In order to achieve an electrode impedance of 50 Ohms, which is often desirable for matching to the impedance of the modulation drive or control electronics, the ratio between the width of the top electrode strip and the thickness of the dielectric layer (which includes the optical guiding layer and the two cladding layers) should be approximately 3 to 4, for the polymer dielectric material of this modulator. The strip electrode on top must be sufficiently wide to cover both optical waveguides (i.e., both waveguide arms of the interferometer). These requirements constrain the minimum separation between the two electrodes of the microstrip line for this modulator. The smallest electrode separation reported in these articles is 7.3 μm.
The lateral extent of each EO waveguide is defined by the shallow rib formed in the guiding layer (see FIG. 1b). A disadvantage of this prior art modulator is that since its electrodes contact the entire outer surfaces of the upper cladding and the lower cladding layers, including the entire space between the two EO waveguides, a substantial amount of the modulating RF field still is applied in the regions away from these optical waveguides and away from the shallow ribs formed in the guiding layer. This inefficient use of the applied RF field reduces the modulation efficiency of this prior art modulator. Although the guiding layer comprises an EO material, the upper cladding and lower cladding of these prior art modulators, which are needed to produce optical waveguiding and to confine the guided light away from the metal electrodes, are not comprised of an EO material. However, the waveguided light (or the optical mode of the waveguide) extends substantially into those cladding layers. Thus, only a smaller percentage of that light can be modulated as a result of changes in the refractive index of only the guiding layer, thereby further degrading the modulation efficiency. The thickness of each of the two cladding layers is at least as large as the thickness of the guiding layer. Thus, at most 20-30% of the applied E-field actually overlaps the EO material of this structure.
Another prior electro-optic modulator is described in an article by P. Rabiei and W. H. Steier (“Lithium niobate ridge waveguides and modulators fabricated using smart guide,” Applied Physics Letters, Vol. 86 (2005), p. 161115). FIG. 2 illustrates the structure of a phase-modulation arm, which has a thin slice of lithium niobate (LiNbO3) EO material that is bounded on its upper and lower sides by layers of SiO2 and further bounded by two metal electrodes. The difference between the refractive index of LiNbO3 and the refractive index of the SiO2 cladding materials in these modulators is large. Thus the vertical size of the guided optical mode in this structure is much smaller than the size of the optical mode in the waveguide of Wang and Shi. As a result of the smaller optical mode size, the metal electrodes can be placed closer to the LiNbO3 EO layer. In contrast, the polymer EO material of the modulator of Wang and Shi has a smaller difference between its refractive index and the refractive index of its cladding layers, so the electrodes of the microstrip line must be farther apart. The overall separation between the two electrodes of the modulator of P. Rabiei and W. H. Steier is only 2.7 μm. However, the total thickness of the SiO2 layers is approximately 2.05 μm and occupies most of this electrode-to-electrode separation. Since the microwave dielectric constant of LiNbO3 is approximately 30 but the microwave dielectric constant of SiO2 is approximately 4, only 4% of the applied voltage is dropped across the LiNbO3 material, with the rest of that applied voltage being dropped across the two SiO2 layers. Also, because the LiNbO3 layer is quite thin, a large portion of the guided light extends into the SiO2 material, which is not electro-optically active; as a result, the modulation efficiency is reduced.
For the modulator of P. Rabiei and W. H. Steier, a shallow rib is formed in the Z-cut LiNbO3 slice to provide some lateral confinement of the optical-waveguided light. The height of this rib is 0.15 μm compared to the 0.5 μm thickness of the portions of the LiNbO3 slice adjacent to that rib. The layers of LiNbO3 and SiO2 as well as the electrodes extend in the lateral direction far beyond the width of the shallow rib. A disadvantage of this modulator is that since its electrodes contact the entire outer surfaces of the upper SiO2 cladding and the lower SiO2 cladding, a substantial amount of the modulating RF field still is applied laterally in the regions away from the optical waveguides and away from the ribs formed in the LiNbO3. This inefficient use of the applied RF field reduces the modulation efficiency of this prior modulator.
Another prior art EO modulator, described in articles by R. Song and W. H. Steier (“Overlap integral factor enhancement using buried electrode structure in polymer Mach-Zehnder modulator,” Applied Physics Letters, Vol. 92 (2008), p. 031103) and by R. Song, et al. (“Analysis and demonstration of Mach-Zehnder polymer modulators using in-plane coplanar waveguide structure,” IEEE J. Quantum Electronics, Vol. 43 (2007), p. 433), is a Mach-Zehnder modulator structure with two EO phase-modulation arms that each comprise an EO polymer core region that is shaped as inverted optical ridge waveguide. The EO polymer core is covered above and below by polymer cladding layers whose optical refractive index is somewhat lower than the optical refractive index of the core material. The core-to-cladding index difference is typically 0.1. The height of the inverted ridge in this prior art structure is 2 μm, which is much greater than the height of the ribs formed in the structures of Rabiei and Steier, of Wang et al., and of Shi et al. However, the difference between the refractive index of the core material and the refractive index of the cladding material is relatively small. Thus, the lateral size of the optical mode is fairly large and the spacing between the electrodes of this structure, which are located at the lateral sides of the EO waveguides was set to 15 μm, to minimize the optical loss from those metal electrodes.
Another prior art EO modulator, described in a patent by R. P. Moeller and J. H. Cole (“Low loss bridge electrode with rounded corners for electro-optic modulators,” U.S. Pat. No. 7,426,326) and in a patent by J. H. Cole, R. P. Moeller and M. M. Howerton (“Low loss electrodes for electro-optic modulators,” U.S. Pat. No. 7,224,869), is a Mach-Zehnder interferometric modulator whose lithium niobate EO material in its two phase-modulation arms are poled in opposite directions. This modulator has a center electrode that includes a pair of protruding portions that point toward and abut a pair of optical waveguides formed in a lithium niobate substrate, as shown in FIG. 3a. In the structure of Moeller and Cole (see FIG. 3a), the protrusions of the center electrode have rounded corners but in the structure of Cole, et al. (see FIG. 3b), the protrusions of the center electrode have square corners. Both of these protruding portions of the center electrode are located on a common top side of the optical waveguides. These two optical waveguides are the two phase-modulation arms of the interferometer. The center electrode with the protruding portions functions as the center conductor of a coplanar-waveguide (CPW) RF transmission line structure. Ground electrodes are disposed on either lateral side of the center electrode. Since both the active, center electrode and the ground electrodes of this CPW electrode structure are located on a common side of the optical waveguides but both optical waveguides are located only beneath the center electrode, the modulating E-field lines must also traverse large regions of lithium niobate substrate that are outside of the optical waveguides. The voltage dropped across these regions outside the optical waveguides does not contribute to the modulation of the light.
Each of the optical waveguides of this prior art modulator is formed in an optical ridge structure that protrudes from the substrate of Z-cut lithium niobate EO material. Because of the high RF dielectric constant of the LiNbO3 EO material, the optical ridges help to direct a greater percentage of the RF electric-field lines through the optical waveguides. Also, the two protrusions in the center electrode direct much of the E-field lines through the two optical waveguides that are located beneath those protrusions and away from the portions of the center electrode that is between those two optical waveguides, to improve the modulation efficiency achieved with this structure. These two prior art patents describe a Mach-Zehnder interferometric modulator in which the two optical waveguides of the pair have their EO material poled in opposite directions. But since the optical waveguides of this prior modulator are quite thick, the poling must remain relatively uniform over the greater thickness of those optical waveguides. This constraint limits how close the two optical waveguides can be spaced from each other, since the direction of the poling of the Z-cut lithium niobate substrates gradually departs from being perpendicular to the surface as the distance from that surface (generally the surface facing the metal electrodes) increases. Thus, the two oppositely poled optical waveguides are spaced far apart and the center electrode must be quite wide. To main a desired impedance, such as 50 Ohms, for the coplanar-waveguide transmission line formed from this center electrode and two ground electrodes, the lateral spacing between the center electrode and a ground electrode is large. As a result, substantial voltage is dropped across the regions outside the optical waveguides and does not contribute to the modulation of the light in the waveguides.
In the structures of Moeller and Cole and of Cole, et al., a low-refractive-index oxide buffer layer is located between the center electrode and the lithium niobate waveguide beneath that electrode in order to reduce the optical attenuation by confining the waveguided light away from the light-absorbing metal material. This oxide buffer, whose dielectric constant is much smaller than the dielectric constant of lithium niobate, further reduces the E-field intensity at the optical waveguide that would result from a voltage applied between the center electrode and a ground electrode. Most prior lithium niobate modulators have an oxide buffer layer between the metal electrode and the lithium niobate EO material of the optical waveguide. Since the lithium niobate waveguides are generally formed by diffusing some material such as titanium into a lithium niobate substrate through the top surface of that substrate, the region of higher refractive index is located near the top of that waveguide structure. Addition of a buffer (or cladding) layer of a material such as silicon dioxide, which has a much lower optical refractive index than lithium niobate, confines the guided light further into the lithium niobate material and away from the metal electrode that is on the opposite side of that buffer layer, to reduce the unwanted absorption of the guided light by the metal electrode. However, much of the applied voltage can be dropped across the buffer layer, because of the low dielectric constant of that buffer in comparison to the dielectric constant of lithium niobate, and thus the E-field at the optical waveguide is reduced.
FIG. 4a shows an electrode structure for a Mach-Zehnder interferometric modulator that is described by Noguchi, et al. (see “Millimeter-wave Ti—LiNbO3 optical modulators,” J. Lightwave Technology, vol. 16, no. 4 (1998), p. 615). With this prior art structure, the center-conductor electrode of the CPW transmission-line lies above one phase-modulation arm and one of the ground electrodes lies above the other phase-modulation arm. As a result, an applied voltage produces E-field vectors that have opposite polarity in the two arms, resulting in push-pull modulation even though the EO materials of both arms have the same poling. Since the CPW structure has E-field lines that go between one center electrode and two ground electrodes, which are on the two lateral sides of the center electrode, the E-field strength at the EO waveguide that is near the ground electrode of this prior structure is only approximately one-half the E-field strength at the EO waveguide that is near the center electrode. Thus, the overall push-pull modulation efficiency is reduced. FIG. 4b shows results obtained by Noguchi, et al. that describe the dependence of a modulator voltage figure-of-merit, VπL and the dependence of the electrode characteristic impedance on the thickness of the oxide buffer. These results indicate that the thick buffer layer is helpful for achieving a value for the electrode impedance that is matched to 50 Ohms. These results also show that VπL increases as the buffer layer is made thicker. The value for Vπ, the applied voltage required to achieve π phase shift for a phase modulator length of L, is higher for a thicker buffer because the E-field at the EO waveguide is lower.
A prior art electrode structure for a modulator constructed from III-V semiconductor EO material is illustrated in FIG. 5 and is described in an article by J. H. Shin, S. Wu and N. Dagli (“35-GHz bandwidth, 5-V-cm drive voltage, bulk GaAs substrate removed electrooptic modulators,” IEEE Photonics Technology Letters, vol. 19, no. 18 (2007), p. 1362). This structure achieves, inherently, a push-pull drive configuration such that the changes in the refractive index of the EO material in the two EO waveguide arms of a Mach-Zehnder interferometer have opposite sign when a voltage is applied to the electrode. Each EO waveguide has one electrode located above it and another electrode located beneath it. Thus the light in the waveguide can experience the maximum E-field, for voltage-efficient modulation. The electrode structure of the two EO waveguides is a coplanar waveguide (CPW) RF transmission line whose center or signal electrode is electrically connected to the electrode located on top of a first of the two EO waveguides but is electrically connected to the electrode located beneath the second EO waveguide. This connection of the signal electrode, together with having one ground electrode of the CPW transmission located beneath the first EO waveguide and the other ground electrode of the CPW transmission line located above the second EO waveguide, achieves the push-pull drive. However, such an electrode configuration requires that the original substrate of the modulator material be removed in order to provide the necessary access to both the top and the bottom sides of the EO waveguides. Also, a portion of the metal electrode must extend from the top of the structure to the bottom of the structure, which complicates their fabrication process.
Another prior art III-V semiconductor modulator achieves push-pull modulation without needing to have its substrate removed (unlike the structure of FIG. 5) and also without needing to have oppositely poled EO material (unlike the structures of FIGS. 1a and 3a). This prior art structure is illustrated in FIG. 6 and is described in a paper by S. Akiyama, et al. (“Wide-wavelength-band (30 nm) 10-Gb/s operation of InP-based Mach-Zehnder modulator with constant drive voltage of 2 Vpp,” IEEE Photonics Technology Letters, vol. 17, no. 7 (2005), p. 1408). For this structure, the thickness of the multiple-quantum-well (MQW) optical waveguide core is 0.5 μm. The slotline electrode of this structure places one metal electrode over one arm of the Mach-Zehnder interferometric modulator and the other metal electrode over the other arm of that optical interferometer. The n-InP lower cladding layer serves as an electrically conductive path between those two metal electrodes. The p-InP upper cladding layer, which is present only above the MQW core region of each EO waveguide arm, also is electrically conductive. Thus, the modulation voltage is established primarily across the MQW core regions of the two arms and the E-field lines are pointed in opposite directions in the two optical-waveguide arms. This structure can achieve voltage efficient push-pull modulation because the gap between the conductive cladding layers is small. However, the overall modulation efficiency of a modulator depends not only on the voltage efficiency but also on the overlap between the optical mode of the light to be modulated and the active EO material. For this prior modulator, only the MQW core region of the waveguide has its refractive index modulated by the applied voltage. But a large portion of the optical mode overlaps the electrically conductive cladding regions instead of overlapping the undoped MQW core region. Thus, the modulation efficiency is degraded.
The semiconductor modulator of FIG. 6 has a conductive n-InP cladding layer that provides an electrically shunting path between the two driven electrodes of the slotline that are located at the top of the modulator. However, because the values for the dielectric constant of the semiconductor material at microwave or millimeter-wave frequencies and at optical frequencies are similar, the series electrical connection of two capacitances that occurs because of the shunting path actually makes the velocity match of the optical and RF waves poorer. Thus, the slotline electrode structure of this prior modulator of FIG. 6 needs to add capacitively loading segments of the RF transmission line in order to increase the velocity of the RF wave to match the velocity of the optical wave. The EO modulation structure of this prior modulator is placed only in capacitively loading segments of the RF transmission line. The modulation of the waveguided light occurs only in these capacitively loading sections and there is no modulation of the light occurring in the segments of EO waveguide between these capacitively loading portions. As a result, the overall length of the modulator must be increased. According to the article by Akiyama, et al., the fractional length of the modulated portion of each phase modulation arm is 0.56. The modulation structure of FIG. 5 likewise can be formed in only a portion of the overall length of the phase-modulation arms of the Mach-Zehnder modulator if 50 Ohm impedance and velocity match also are desired. According to the article by Shin, Wu and Dagli, the fractional length of the modulated portion of the phase-modulation arm is only 0.47 when the structure achieves both 50 Ohms impedance and velocity match between the optical and RF waves. Thus, the modulation efficiency for these two modulators is poorer by approximately a factor of two compared to a structure that can have its EO waveguide interact with the entire length of the electrode structure.
To provide a point of comparison to the prior art push-pull modulation structures described above, FIGS. 7a and 7b illustrate another prior electrode structure constructed from III-V semiconductor materials. This structure is described in a paper by K. Tsuzuki, et al. (“A 40-Gb/s InGaAlAs—InAlAs MQW n-i-n Mach-Zehnder modulator with a drive voltage of 2.3 V,” IEEE Photonics Technology Letters, vol. 17, no. 1 (2005), p. 46). This prior art modulator does not have a push-pull electrode structure and, instead, two separate voltage waveforms of opposite polarity must be applied to the electrodes of its two phase-modulation arms in order to achieve push-pull modulation. Thus, the power of the input modulation signal would need to be doubled since that modulation signal is used to produce two separate modulation-control waveforms, with one of those modulation-control waveforms delivered to each of the two phase-modulation arms. This structure has separate RF coplanar-waveguide (CPW) transmission line electrodes associated with each of the two arms of the Mach-Zehnder interferometer modulator. For each arm of the interferometer, the active or signal electrode is located above the optical waveguide, which is formed as a tall ridge etched from the semiconductor material, and the return or ground electrodes of the RF coplanar-waveguide transmission line are located beside the tall ridge. The waveguide core region, comprising a multiple-quantum-well (MQW) structure, is sandwiched between lower refractive-index cladding layers that consist of a combination of a semi-insulating InP layer and an n-doped InP layer combination or that consists of just an n-doped InP layer. The n-doped InP layers are electrically conductive and thus the modulating E-field is established across the combined thickness of the MQW active layer and the semi-insulating InP layer, which gives a total thickness of 1.3 μm. The electro-optic modulation coefficient of MQW material is substantially higher than the electro-optic modulation coefficient of its constituent III-V semiconductor materials. With this structure, the full-scale modulation voltage (Vπ for a Mach-Zehnder modulator) is reduced to a value of 2.2 volts, with that voltage applied to only one of the two phase-modulation arms, which have a length of only 3 mm. A weakness of this prior art structure is that since its EO waveguide ridge comprises semiconducting material, the sides of the semiconductor ridge must be covered with a dielectric spacer, such as BCB, which limits the minimum size of the gap that can be formed between a signal electrode and its associated ground electrode.
The optical loss of the III-V semiconductor modulators that have MQW EO waveguide core regions is quite high. The article of Akiyama et al, reported an optical insertion loss of 10 dB for their Mach-Zehnder modulator that has the modulation structure of FIG. 6 and a length of 3.6 mm for its phase-modulation arms. The article of Tsuzuki et al. did not even provide a number for the optical loss of its modulation structure. For comparison, the optical propagation loss of the EO phase-modulation arms of the structure of FIG. 5 is only approximately 3 dB/cm. The structure of FIG. 5 has undoped, bulk AlGaAs/GaAs/AlGaAs EO material instead of an MQW core layer and doped cladding layers.
The electro-optic modulation coefficient of III-V semiconductor EO material is quite small (generally 1-2 μm/volt) and is much smaller than the electro-optic modulation coefficient of LiNbO3 EO material (which has a value of approximately 30 μm/volt) or of temperature-stable EO polymer material (which can have a value as large as 50-100 μm/volt). To compensate for its small electro-optic modulation coefficient, the electrode gap for a III-V semiconductor structure must be made very small (compared to the gap in LiNbO3 modulators and in many EO polymer modulators) in order to achieve a reasonably low full-scale modulation voltage, Vπ, and also conductive cladding layers are needed to establish that narrow gap. Such a construction is accompanied by deficiencies such as the following. The overlap of the optical field with the modulating E-field is poor since the optical field extends far into the conductive cladding whose refractive index is not modulated (because there is negligible voltage drop across the conductive cladding, and thus negligible E-field). There is unwanted optical attenuation from the conductive cladding because of free-carrier absorption of the light, especially in p-type cladding. There also is poor coupling of the waveguided light in the modulator with the light in an optical fiber to which the modulator may be connected (because the size of the optical mode in those semiconductor EO waveguides is so small).
Lithium niobate has a large electro-optic coefficient compared to InP-based and GaAs-based III-V materials. However, voltage efficient electrode structures like those developed for the III-V modulators have not been used for lithium niobate modulators. One reason is that III-V materials are semiconductors and thus electrically conductive optical waveguide cladding layers can be formed using those III-V materials. In contrast, lithium niobate is an electrical insulator. There are no electrically conductive materials that can be used with lithium niobate and that also have reasonably high optical transparency for the 1550 nm wavelength light typically used in optical links that contain the modulators. For example indium tin oxide absorbs light having wavelengths longer than 1000 nm. Furthermore, any potential transparent and conductive cladding would not contribute to the modulation of the percentage of the guided light whose mode distribution overlaps the cladding material, since there would be negligible voltage drop across that conductive material.
Polymer EO modulators suffer from some of the same limitations as lithium niobate in that conductive polymers with good transparency to 1550 nm wavelength light are not available. Thus, the cladding layers of typical polymer modulators are insulating. Also, typical polymer cladding materials that have low optical loss are not electro-optically active.
The oxide buffer layer of the prior lithium niobate modulators serves as a one-side cladding layer that reduces the overlap of the guided light with the metal electrodes above it, to reduce the optical loss. The additional voltage drop across this oxide buffer layer reduces the E-field level at the EO material underneath that oxide buffer, thereby reducing the voltage efficiency of the modulator.
For lithium niobate EO modulation structures whose electrodes are electrically connected in series, like the prior structure of Noguchi, et al., the width of the center conductor of the CPW transmission line is approximately equal to the width of the EO waveguide under it. For this prior structure, a thickness of approximately 1 μm is desirable for the oxide layer, even though that thicker oxide layer reduces the modulation efficiency and increases the value for VπL. In contrast to the series-configured structures, the effective width of the center conductor of the EO modulation structures whose electrodes are electrically connected in parallel is at least doubled, even when that center conductor has protrusions that extend toward the EO waveguide ridges, as in the structures of Moeller and Cole. One might expect that a larger inter-electrode gap or an even thicker oxide layer would be needed for such a parallel-configured structure to achieve a characteristic impedance of approximately 50 Ohms and also to even approach achieving a velocity match for the propagating RF and optical fields.
The path traversed by the E-field lines from the center conductor to the ground electrodes of a CPW transmission line passes not only through the EO waveguides beneath the center conductor but also through additional lithium niobate material beneath and to the sides of those EO waveguides. The E-field strength resulting from an applied voltage is inversely proportional to the length of the path between the electrodes across which that voltage is applied. To improve the modulation efficiency, it is desirable to reduce the path of the E-field lines, in opposition to the practice required for the CPW transmission lines with wide center conductors.
The electrode-to-electrode gaps achievable with the lithium niobate modulation structures of FIGS. 3a, 3b and 4a are much larger than the size of the optical mode for the light in the EO waveguides. Thus, much of the applied voltage is dropped in a voltage-inefficient manner in portions of the lithium niobate substrate that do not contain the light to be modulated.